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The 2-dimensional uncertain linguistic variable (2DULV) can depict decision-makers’ subjective assessments on the reliability of given evaluation results, which is a valid and practical tool to express decision information. In this study, we develop an improved MABAC method with 2DULVs to handle multiattribute group decision-making (MAGDM) problems where the weight information of attributes is unknown. First, some related theories of 2DULVs and the basic procedure of the MABAC method are briefly reviewed. Then, the maximum comprehensive evaluation value method is extended to 2DULVs to obtain combination weights of attributes, in which the subjective weights are determined according to the best–worst method (BWM) and the objective weights are calculated by the maximum deviation method. Besides, the generalized weighted average operator for 2DULVs (2DULGWA) is utilized to aggregate the evaluation information given by all experts. Finally, an improved MABAC for 2DULVs (2DUL-MABAC) is proposed, and an example is carried out to explain the validity of the proposed approach.

In this paper, the idea of the bipolar Pythagorean fuzzy sets (BPFSs) and its activities, which is a generalization of fuzzy sets, bipolar fuzzy sets (BFSs), intuitionistic fuzzy sets and bipolar intuitionistic fuzzy sets is proposed, with the goal that it can deal with dubious data all the more flexibly during the process of decision making. The key objective of this research paper has presented another variant of the Pythagorean fuzzy sets so called BPFSs. In bipolar Pythagorean fuzzy sets, membership degrees are satisfying the condition $$0 \le \left( {\mu_{p}^{ + } \left( x \right)} \right)^{2}$$ + $$\left( {v_{p}^{ + } \left( x \right)} \right)^{2} \le 1$$ and $$0 \le \left( {\mu_{p}^{ - } \left( x \right)} \right)^{2}$$ + $$\left( {v_{p}^{ - } \left( x \right)} \right)^{2} \le 1$$ instead of $$0 \le \left( {\mu_{p} \left( x \right)} \right)^{2}$$ + $$\left( {v_{p} \left( x \right)} \right)^{2} \le 1$$ as is in Pythagorean fuzzy sets and $$0 \le \mu_{p} \left( x \right)$$ + $$v_{p} \left( x \right) \le 1$$ as is in the intuitionistic fuzzy sets. Here, negative membership degree means the certain counter-property comparing to a bipolar Pythagorean fuzzy set. Also, the BPFSs weighted average operator and the BPFSs weighted geometric operator to aggregate the BPFSs is developed here. Further a multi attribute decision making technique is developed and the proposed aggregation operators are used. Finally, a numerical methodology for execution of the proposed system is introduced.

The objective of this paper is to develop Pythagorean fuzzy (PF) aggregation operators, utilizing the concept of power aggregation operators through Schweizer and Sklar (SS) operations. A series of aggregation operators, viz., PF SS power average operator, PF SS power weighted average operator, PF SS power geometric operator, and PF SS power weighted geometric operator under PF environment is proposed in this paper. The developed operators possess the capacity to make information aggregation technique more flexible than other existing operators due to the presence of SS t-norms and t-conorms in PF environment. Also, for the appearance of power aggregation operator, the developed operators contain the capability to eliminate effects of unreasonable data from biased decision makers by considering interrelationships among the fused arguments. Several properties of the proposed operators are studied and a method for solving multi-attribute decision-making problems under PF context is developed. To illustrate the proposed method and to show its efficiency, an example, studied previously, is solved and compared with existing methods.

In this paper, we define aggregation operators for trapezoidal cubic linguistic fuzzy sets which includes generalized cubic linguistic fuzzy averaging (geometric) operator, generalized trapezoidal cubic linguistic fuzzy weighted averaging (GTrCLFWA) operator, generalized trapezoidal cubic linguistic fuzzy weighted geometric (GTrCFWG) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted average (GTrCLFOWA) operator, generalized trapezoidal cubic linguistic fuzzy ordered weighted geometric (GTrCLFOWG) operator, generalized trapezoidal cubic linguistic fuzzy hybrid averaging (GTrCLFHA) operator and generalized trapezoidal cubic linguistic fuzzy hybrid geometric (GTrCLFHG) operator. Furthermore, we relate these aggregation operators to develop an approach to multiple attribute group decision-making with trapezoidal cubic linguistic fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach.

Hesitant fuzzy linguistic term set is defined in hesitant fuzzy linguistic decision frameworks in which all decision makers are agreed on the primary linguistic scale and its membership functions; however, this situation does not always happen, because words mean different things to different people or there are some linguistic term sets with different semantics for different people. Hence, normalization of linguistic information is necessary. Inspired by normalizing linguistic information based on 2-tuple linguistic model, in this paper, the concept of generalized hesitant fuzzy linguistic term set is proposed when decision makers are not agreed on the primary linguistic scale and its membership functions, which is an extension of hesitant fuzzy linguistic term set. Then, t-norms and t-conorms are utilized to define new operations on generalized hesitant fuzzy linguistic term sets and their properties are discussed. Based on these new operations, the likelihood-based comparison relation of generalized hesitant fuzzy linguistic term sets is presented, which is an extension of the likelihood-based comparison relation of hesitant fuzzy linguistic term sets. Accordingly, the generalized hesitant fuzzy linguistic weighted average operator, generalized hesitant fuzzy linguistic weighted geometric operator, generalized hesitant fuzzy linguistic ordered weighted average operator and generalized hesitant fuzzy linguistic ordered weighted geometric operator are provided to fuse generalized hesitant fuzzy linguistic term sets in linguistic decision making. A case study is used to illustrate the practicality of the method based on generalized hesitant fuzzy linguistic term sets and compare with Lee and Chen’s method, Rodriguez’s method and Wei’s method. It seems that the method based on generalized hesitant fuzzy linguistic term sets is flexible and useful method for hesitant fuzzy linguistic decision making.

In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.

In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we have investigated the multiple attribute decision-making problems with bipolar fuzzy information. Motivated by the Hamacher operations, we have proposed bipolar fuzzy Hamacher weighted average operator, bipolar fuzzy Hamacher ordered weighted average operator, bipolar fuzzy Hamacher hybrid average operator, bipolar fuzzy Hamacher weighted geometric operator, bipolar fuzzy Hamacher ordered weighted geometric operator, bipolar fuzzy Hamacher hybrid geometric operator. We investigate the characteristics and special cases of these operators. Then, we have utilized these operators to develop some approaches to solve the bipolar fuzzy multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we investigate the multiple attribute decision making problems based on the power aggregation operators with hesitant fuzzy uncertain linguistic information. Then, we have developed some power aggregation operators for aggregating hesitant fuzzy uncertain linguistic information: hesitant fuzzy uncertain linguistic power weighted average operator and hesitant fuzzy uncertain linguistic power weighted geometric operator. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the teaching quality in higher education is given to verify the developed approach and to demonstrate its practicality and effectiveness.

© 2019 by the authors. In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

To solve the problem of strong subjectivity and less objectivity of decision-making in distribution network planning scheme caused by qualitative evaluation indices, a model was proposed which combines parabolic ordered weighted average operator (P-OWA) with entropy weight and grey relational analysis (EW-GRA). Firstly, the expert scoring of qualitative indices were reasonably assembled by a P-OWA operator. The whole indices using an entropy weight method. The correlation matrix was obtained according to a grey relation analysis. The grey correlation degree was obtained by weighting. Finally, the optimal scheme was obtained according to the result of ranking. By applying this method to an actual case, its effectiveness was verified by comparing with other methods.

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

Simplified neutrosophic sets (SNSs) can effectively solve the uncertainty problems, especially those involving the indeterminate and inconsistent information. Considering the advantages of SNSs, a new approach for multi-criteria decision-making (MCDM) problems is developed under the simplified neutrosophic environment. First, the prioritized weighted average operator and prioritized weighted geometric operator for simplified neutrosophic numbers (SNNs) are defined, and the related theorems are also proved. Then two novel effective cross-entropy measures for SNSs are proposed, and their properties are proved as well. Furthermore, based on the proposed prioritized aggregation operators and cross-entropy measures, the ranking methods for SNSs are established in order to solve MCDM problems. Finally, a practical MCDM example for coping with supplier selection of an automotive company is used to demonstrate the effectiveness of the developed methods. Moreover, the same example-based comparison analysis of between the proposed methods and other existing methods is carried out.

With respect to dynamic multi-attribute group decision-making (DMAGDM) problems, where attribute values take the form of intuitionistic fuzzy values (IFVs) and the weights (including expert, attribute and time weights) are unknown, the dynamic intuitionistic fuzzy power geometric weighted average (DIFPGWA) operator and the improved IFVs’ GM(1,1) prediction model (IFVs-GM(1,1)-PM) are proposed. First, the concept of IFVs, the operational rules, the distance between IFVs, and the comparing method of IFVs are defined. Second, the DIFPGWA operator and the improved IFVs-GM(1,1)-PM are defined in detail. Third, corresponding decision-making (D-M) steps are proposed. Three kinds of weights are given by the proposed determination method. Finally, an example is given to prove the effectiveness and superiority of the proposed decision-making method.

With respect to the multiple attribute decision making problems in which the attribute values take the form of the 2-dimension uncertain linguistic information, a new method based on the generalized hybrid operators is proposed. Firstly, the definition, properties, expectations and ranking method of 2-dimension uncertain linguistic information are introduced, and the operational laws the 2-dimension uncertain linguistic information are defined. Then some aggregation operators, including 2-dimension uncertain linguistic generalized weighted average operator, 2-dimension uncertain linguistic generalized ordered weighted average operator, and 2-dimension uncertain linguistic generalized hybrid weighted average operator, are developed, and some properties and special cases of them are also discussed. Finally, these operators are applied to multi-criteria decision making and an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.

In this paper, we develop a new linguistic aggregation operator based on the cloud model for solving linguistic group decision-making problem. First, an improved generating cloud method is proposed so as to transform linguistic variables into clouds, which modifies the limitation of the classical generating cloud method. We then address some new cloud algorithms, such as cloud possibility degree and cloud support degree which can be respectively used to compare clouds and determine the weights. Combining the cloud support degree with power aggregation operator, we develop a new cloud aggregation operator dubbed the cloud generalized power ordered weighted average (CGPOWA) operator. We study the properties of the CGPOWA operator and investigate its family including a wide range of aggregation operators such as the CGPA operator, CPOWA operator, CPOWGA operator, CPWQA operator, CWAA and CWGA operator. Furthermore, a new approach for linguistic group decision-making is presented on the basis of the improved generating cloud method and CGPOWA operator. Finally, an illustrative example is provided to examine the effectiveness and validity of the proposed approach.

Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.

This study presents an innovative approach to develop a course specification that considers the effect of the covered topics in a course on the entire program learning outcomes. This study presents a practical methodology enabling instructors to design an efficient course specification based on the national academic accreditation and assessment standards of the Kingdom of Saudi Arabia. Fuzzy linguistic variables are aggregated using the induced unbalanced linguistic ordered weighted average operator.

Despite the growing trend in intelligent transportation systems applications, there are still many problems waiting for an accurate solution such as traffic flow forecasting. In this paper, based on real-time data provided by dual loop speed traps detectors at given slot of time, we propose a cloud-based data collection method which is aimed to improve prediction accuracy. To reach this level of accuracy, two traffic parameters were introduced, the average speed and the foreseen arrival time between two vehicles. By adopting Choquet integral operator, these parameters can subsequently aggregate to busiest traffic parameters. Afterwards, a simple linear regression is applied for a dual purpose, the first to predict the traffic flow, then prove that there is a relationship between derived busiest arrival time and the traffic flow. Moreover, the simulation charts demonstrates that the forecasts by the Choquet operator ensure an accurate results to the real-time data. In contrast, the forecasts using weighted average operator lead to low accuracy compared with real-time data.